With three weeks of fighting in Damascus signaling the accelerating erosion of the Assad regime’s control of Syria, Western diplomats are pressing the exiled opposition leadership to take charge of governing rebel-held areas. “We’re telling them, ‘You need to get in on the ground; you need to have face-to-face meetings,’ ” Jon Wilks, Britain’s envoy to the Syrian opposition, told TIME in Marrakesh Tuesday night, on the sidelines of an international Friends of the Syria summit. “No more meeting in five-star hotels in Marrakesh.”

After two days huddled in talks with Syrian rebel leaders in a luxury golf resort outside the Moroccan tourist mecca, dozens of foreign ministers and diplomats from Western and Arab countries anointed the exiled Syrian National Coalition — formed last month in Qatar — as the effective successors to Assad’s regime. “Assad has lost legitimacy and should stand aside to allow the launching of a sustainable political transition process,” said the final statement of the conference on Wednesday. The new coalition, diplomats explained, is now “the umbrella organization under which Syrian opposition groups are gathering.”

The pressure to start delivering real services to exhausted Syrians increased markedly overnight, after President Obama told ABC’s Barbara Walters on Tuesday that the U.S. is recognizing the new coalition as the representatives of the country’s 20 million people. Obama’s decision echoes those by France, Britain and the Gulf countries, and was followed Wednesday by a formal invitation for rebel leaders to visit Washington as soon as possible

Despite their new diplomatic status among Western and Arab powers, however, one of the key rebel demands — for more and better weapons — has not yet been granted. The New York Times reported Monday that Administration officials allege that Assad’s forces had, over the past six days, begun firing Scud missiles at rebel fighters. Nonetheless, while arms are being sent in from Qatar, Turkey and Saudi Arabia, European countries are forbidden under a three-month E.U. arms embargo from supplying weapons to the rebels, or the regime. French Foreign Minister Laurent Fabius told reporters in Marrakesh that the embargo would soon be reviewed. But U.S. officials have made it clear they are in no rush to arm the fighters, fearing that weapons could end up in the hands of extremists. Despite formally recognizing the National Coalition, the U.S. is determined to avoid directly assisting the military struggle. “Our position has not changed on that issue,” Deputy U.S. Secretary of State William Burns told reporters here. “Our position remains non-lethal assistance.”

On Monday, the State Dept. declared the Nusra Front, a Syrian rebel outgrowth of Iraq’s al-Qaeda affiliate, a foreign terrorist organization — a move that drew sharp criticism from rebel leaders. Some of those in Marrakesh insisted that the rebellion cannot afford divisions among the fighters waging the war, and expressed resentment that the U.S. is attempting to dictate which ones are acceptable. “All the guns of the rebels are aimed at bringing down the tyrannical, criminal regime,” the president of the new Syrian coalition Sheik Moaz al-Khatib, a cleric from Damascus, said in his address to the conference. “There is no harm in anyone having religion as a motivation to liberate his country.”

Despite having secured the imprimatur of world leaders, in fact, the National Coalition’s biggest challenge lies in winning credibility at home. Rebel fighters have long expressed cynicism about the exile leaders’ comfortable distance from the frontline — a criticism unlikely to be dispelled by the luxurious setting of the Marrakesh meeting — accusing them of all talk and no action.

But President Obama’s statement on Tuesday helped focus the meeting on the nitty-gritty details of Syria’s end game, and on the challenges of governing those parts of the country liberated from the regime’s control. The Coalition’s hodge-podge collection of technocrats — some exiled for many years — has failed, thus far, to announce a provisional government. That’s in sharp contrast to the Libyan example, where the **rebels’ National Transitional Council was formed long before the Gaddafi regime’s collapse, and effectively ran half of Libya for months while the war raged on.

A patchwork body of different factions, the Syrian coalition is still wrangling over who will ultimately run the country. “We are now discussing the idea of a government and the basis on which it should be established,” Coalition vice president George Sabra told TIME early Wednesday. “We hope we’ll reach an agreement on a government within a month.”

That government will have its work cut out for it: Much of Syria lies in ruins, after 21 months of calamitous fighting that has killed an estimated 40,000 people, and destroyed thousands of schools, businesses, and entire neighborhoods. The U.N. estimates about two million homes have been damaged or destroyed, and that half a million Syrians are currently living as refugees, mostly in Lebanon, Jordan and Turkey.

In Marrakesh on Wednesday, Saudi Arabia pledged $100 million in humanitarian relief funds to the Coalition, while Secretary Burns said the U.S. would give $13 million above what Washington had originally provided. Those funds would be channeled through a new Coalition-run humanitarian assistance group, formed earlier this month with assistance from full-time staff from the U.S., Britain, France and Italy.

Western diplomats worry that the rebels are too focused on immediate relief, and are not giving enough attention to how Syria will be governed once Assad falls. The fear is that Assad’s collapse could come faster than exiled leaders expect, potentially producing a lethal power vacuum that

could extend the civil war for many years. “Right now, it would be very difficult for them to pick up the reins once the regime falls,” Wilks, the British envoy. “They have to focus on what they will do if the regime falls tomorrow.”

Coalition leaders say their plan is to try and inject money into rebel-held areas — about 40% of the country — coordinating more tightly with local councils, to try piece together parts of the shattered economy. They estimate it will cost them about $500,000 a month to run towns and villages in those areas, until Assad falls. The exiles’ ability to win support from Syrians on the ground after Assad goes could hang on how they perform during the final months of the fighting. “We have to start paying people salaries and getting officials to come back to work,” says Abrahim Miro, a Syrian economist on leave from his job in the Netherlands, who is economic advisor to the coalition. “About 2,000 businesses have closed just in Aleppo alone. We need to get in there and open them up again.”